What's the pitch of your roof?
Enter rise and run or an angle, get the pitch, degrees and rafter length instantly.
Rise and run in the same units — inches, feet or centimeters.
How do I calculate roof pitch?
Pitch is how many inches the roof rises for every 12 inches of horizontal run. Measure the rise over any run and scale it to 12: a roof that rises 4 feet over a 16 ft run has a pitch of 4 ÷ 16 × 12 = 3, or 3/12. The calculator does the same with any rise and run in matching units.
How do I convert roof pitch to degrees?
The angle is the arctangent of rise ÷ run. A 6/12 roof is arctan(0.5) = 26.6°, 4/12 is 18.4°, 8/12 is 33.7° and 12/12 is exactly 45°. The table above lists every pitch from 1/12 to 18/12.
How do I measure the pitch of my roof?
From the attic, hold a level against the underside of a rafter, mark 12 inches along the level, and measure straight up from that mark to the rafter — that is the rise. Outside, do the same on the roof surface or on a gable-end rake board.
How do I calculate rafter length?
Take half the building's span, add the overhang, and multiply by the pitch factor. For a 24 ft wide house with a 6/12 roof and 1 ft overhangs: (12 + 1) × 1.118 = 14.53 feet, before the ridge board and plumb cuts.
What is a common roof pitch?
Most houses in the US have pitches between 4/12 and 9/12. Below 4/12 is a low-slope roof — asphalt shingles need extra underlayment down to 2/12 and are not used below it. Above 9/12 is steep and needs roof jacks to work on safely.
How do I find the roof area from the footprint?
Multiply the footprint (the horizontal area under the roof) by the pitch factor. A 30 × 40 ft building is 1,200 ft². With a 6/12 roof the factor is 1.118, so the sloped area is 1,342 ft², before overhangs and waste. Hips and valleys do not change this number, but they do change the lengths of the framing members and the amount of flashing.
Pitch, angle and grade
Three ways describe the same slope. Pitch is the rise in inches over a 12-inch run, written as x/12. The angle is arctan(rise ÷ run). Grade is rise ÷ run as a percentage. For example, a 6/12 roof is 26.6°, a 50% grade and has a pitch factor of 1.118. A 4/12 roof is 18.4° (33.3%) with factor 1.054, and a 9/12 roof is 36.9° (75%) with factor 1.250. The factor is √(1 + (rise ÷ run)²), the length of the slope for each foot of horizontal run.
A worked example
A roof that rises 5 feet over a 12 foot run has a pitch of 5 ÷ 12 × 12 = 5, or 5/12. The same pitch measured on a 24 ft wide house applies to half the span, 12 ft. For a 24 ft wide house with a 6/12 roof and 1 ft overhangs the rafter length is (12 + 1) × 1.118 = 14.53 ft. The run in the pitch is always the horizontal distance from the outer wall to the ridge, which is half the span for a symmetrical gable roof.
Common mistakes
Using the whole span as the run is the first mistake: for a gable roof the run is half the span. The second is mixing up the units of rise and run; both must be in the same unit before the ratio is scaled to 12. A third is treating the pitch as the angle, since 12/12 is 45° and not 12°. And a calculated rafter length is the length along the slope to the plumb cut; the ridge board thickness and the tail cuts are extra, so check them against the framing plan.
Sources: the geometry of the right triangle, as in OpenStax Algebra and Trigonometry; shingle underlayment guidance from the manufacturers’ installation instructions. Related: roof calculator, rafter length calculator, right triangle calculator and slope calculator.